This paper reviews in detail Francisco Varela's work on subjectivity and consciousness in the biological sciences. His original approach to this "hard problem" presents a subjectivity that is radically intertwined with its biological and physical roots. It must be understood within the framework of his theory of a concrete, embodied dynamics, grounded in his general theory of autonomous systems. Through concepts and paradigms such as biological autonomy, embodiment and neurophenomenology, the article explores the multiple levels of circular causality assumed by Varela to play a fundamental role in the emergence of human experience. The concept of biological autonomy provides the necessary and sufficient conditions for characterizing biological life and identity as an emergent and circular self-producing process. Embodiment provides a systemic and dynamical framework for understanding how a cognitive self--a mind--can arise in an organism in the midst of its operational cycles of internal regulation and ongoing sensorimotor coupling. Global subjective properties can emerge at different levels from the interactions of components and can reciprocally constrain local processes through an ongoing, recursive morphodynamics. Neurophenomenology is a supplementary step in the study of consciousness. Through a rigorous method, it advocates the careful examination of experience with first-person methodologies. It attempts to create heuristic mutual constraints between biophysical data and data produced by accounts of subjective experience. The aim is to explicitly ground the active and disciplined insight the subject has about his/her experience in a biophysical emergent process. Finally, we discuss Varela's essential contribution to our understanding of the generation of consciousness in the framework of what we call his "biophysics of being."